Q 11-09-147JEE MainJEE Main 2019 (12 Jan, Shift 2)Medium
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is $5$ cm and its rotational speed is $2$ rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:
Answer: (B) $2.0$
The free surface of a rotating liquid is a paraboloid with
$$\Delta h = \frac{\omega^2r^2}{2g},\qquad \omega = 2\pi\times2 = 4\pi\ \text{rad/s}$$
$$\Delta h = \frac{16\pi^2\times(0.05)^2}{2\times10} \approx 0.0197\ \text{m} \approx 2.0\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics